The invention relates to a method and a machine for preparing and depositing a packaging sleeve or strip on a palletized load, and consisting in:                forming the sleeve in a preparation station from a flexible plastic film wound flat on at least one storage reel,        taking hold of the sleeve by means of a gripper device equipped with at least one set of grippers movable in the heightwise direction with a vertical translation movement between a raised position and a lowered position,        performing transverse stretching in the raised position by moving the four corners of the sleeve apart by means of the set of grippers,        after stretching, transferring the sleeve to a position above the load situated in a depositing station, the overstretching perimeter then being greater than the pick-up perimeter,        and lowering the sleeve to envelop the load to be packaged.        